The blockings of matrices A and L are identical.
Blocks and are scalars, and
are row vectors,
and and are column vectors. Sub-matrices
, , , and
are square matrices.

The assumption is that bold-face parts of the lower triangular
matrix have already been computed, and have overwritten the
corresponding parts of A . The rest of the matrix has not
been updated at all, and the object of the next step is
to compute the next parts of the lower triangular matrix,
and , overwriting the corresponding parts of
A .
From the above equation, we derive

Thus if and are to be updated
by and , the following step will suffice:

The algorithm of left looking version of Cholesky factorization can be
given as follows using the above equations

Update the current panel according to Equation .

Continue recursively by repartitioning the matrix.

The PLAPACK implementation using global level-2 BLAS is given
in Figure 8.3.
In this code, at the top of the loop, a_1 references the matrix